Gas Laws
Vocabulary
gas |
pressure |
volume |
temperature |
Kelvin |
kinetic energy |
partial pressure |
mm Hg |
atm |
Boyle's Law |
Charle's Law |
Gay-Lussac's Law |
Ideal Gas Law |
ideal gas constant |
diffusion |
Graham's Law |
Important
Identities
°F = °C + 32 and °C =
K = °C + 273 and °C = K - 273
Dalton's Law of Partial Pressure: P_{Total} = P_{1} + P_{2} + P_{3} ...
Boyle's Law for P-V Changes: P_{1} x V_{1} = P_{2} x V_{2} [Inverse Proportion]_{}
Charle's Law for T-V Changes: = [Direct Proportion]
Gay-Lussac's Law for T-P Changes: = [Direct Proportion]
Combined Gas Law: =
The IDEAL GAS
LAW: P x V =
n x R x T |
where R = 0.0821 and n = number of moles of gas
Graham's Law: = _{}
Study Problems
1. Explain whether the two variables in each scenario are directly or inversely related.
(a) What happens to the pressure when gas particles
are added or removed at a constant volume and constant temperature?
(b) What happens to the pressure when the volume is
either increased or decreased at a constant temperature and constant number of
gas particles?
(c) What happens to the pressure when the temperature is either increased or decreased at a constant volume and constant number of particles?
2. For each scenario identify mathematically the change that is described.
(a) A basketball contains 1 mol of gas. What will happen to the pressure if another
1 mol of gas is added to the ball but the temperature and the volume do not
change?
(b) If a gas is compressed from 4 L to 1 L and the
temperature remains constant, what happens to the pressure?
(c) A balloon with a volume of 4 L at the bottom of a
swimming pool expands to a volume of 12 L when out of water. What happens to the pressure in the balloon
if the temperature remains constant?
3. A gas mixture
containing oxygen, nitrogen, and carbon dioxide has a total pressure of 250 mm
Hg. If P= 50 mm Hg, P= 175 mm Hg, what is P? What is the total pressure in atm?
4. Boyle's Law for Pressure-Volume Changes:
(a) The pressure on 2.50 L of anesthetic gas is
changed from 760 mm Hg to 304 mm Hg.
What will be the new volume if the temperature remains constant?
(b) A given mass of air has a volume of 6.0 L at 1
atm. What volume will it occupy at 190
mm Hg if the temperature does not change?
5. Charle's Law for Temperature-Volume Changes:
(a) If a sample of gas occupies 6.8 L at 327 °C, what
is the volume at 27 °C if the pressure does not change?
(b) Five liters of air at -50 °C are warmed to 100
°C. What is the new volume if the
pressure is constant?
6. Gay-Lussac's Law for Temperature-Pressure Changes:
(a) A gas has a pressure of 50.0 mm Hg at 540 K. What is the pressure at 200 K if the volume
does not change?
(b) The pressure in an automobile tire is 2.0 atm at
27 °C. At the end of a journey on a hot
sunny day the pressure has risen to 2.2 atm.
What is the temperature of the air in the tire? (Assume constant volume.)
7. Show how (a) Boyle's law, (b) Charle's law, and (c)
Gay-Lussac's law can be derived from the combined gas law.
8. A 5.0 L air sample at a temperature of -50 °C has a
pressure of 800 mm Hg. What will be the
new pressure if the temperature is raised to 100 °C and the volume expands to
7.0 L?
9. What volume will 12.0 gm of oxygen gas occupy at 25
°C and a pressure of 0.520 atm?
10. What pressure will be exerted by 0.450 mol of a
gas at 25 °C if it is contained in a vessel whose volume is 650 cm^{3}?
11. Answer EITHER (a) or (b). Note that the two questions are different
approaches to the same concept.
(a) No gas exhibits ideal behavior at all temperatures
and pressures. Explain the meaning of
this statement.
(b) At what conditions do real gases behave like ideal
gases? Why?
12. Refer to Figure 12.19 on page 344. What is the value of for CO_{2} at 40 °C and 100 atm?
13. Which gas diffuses faster: hydrogen or
chlorine? How much faster?
14. Calculate the ratio of the velocity of molecular
oxygen to atomic argon at the same temperature.
15. HCl gas is introduced into one end and NH_{3}
gas into the other end of a 5.0 meter long glass tube. Where in the tube will the white ammonium
chloride precipitate form? Draw a
picture of this scenario.
Mastery Problems
16. If 4.50 gm of methane gas (CH_{4}) is introduced into an evacuated 2.00 L container at 35 °C, what is the pressure in the container in atm?
17. A 3.50 L gas sample at 20 °C and a pressure of 650 mm Hg is allow to expand to a volume of 8.00 L. the final pressure of the gas is 425 mm Hg. What is the final temperature of the gas in degrees Celsius?
18. A gas cylinder contains nitrogen gas at 10 atm pressure and a temperature of 20 °C. The cylinder is left in the sun, and the temperature of the gas increases to 50 °C. What is the pressure in the cylinder?
19. Calculate the ratio of the velocity of helium atoms to fluorine molecules at the same temperature.
20. Calculate the number of liters occupied at STP:
(a) 2.5 mol N_{2} (b) 0.600 gm H_{2} (c) 0.350
mol O_{2}
Challenge Problem
Nitroglycerine has a density of 1.59 gm/mL. It explodes to form several gases:
4 C_{3}H_{5}O_{9}N_{3} ---> 12 CO_{2} + 1 O_{2} + 6 N_{2} + 10 H_{2}O
A sealed 1.00 mL container filled with nitroglycerine is detonated. Assuming standard temperature and assuming that the container would not break upon detonation, what is the pressure inside the container in atmospheres?
Review Problem
How many kcal of heat are required to raise 40.0 gm of ice at -12 °C to 130 °C?